The basic task of a range-Doppler imaging system is to estimate the relative reflectivity of a spatial distribution of scatterers. The range-Doppler principle implies that an appropriate signal is radiated and the return signal is processed in order to determine the range (time-delay) and radial velocity (Doppler frequency) of each scattering element of an object. In particular, the presence of a radial velocity gradient across a rigid, rotating object allows one to obtain an image by associating a time delay and Doppler frequency with each point on the object. This technique is more fully discussed in all of the following references: Evans, J. V. and T. Hagfors, Eds., Radar Astronomy, New York, McGraw-Hill (1968); Green, P. E. and R. Price, "Signal Processing in Radar Astronomy", Lincoln Lab. Tech. Rpt., No. 234, October 1960; Leith, E. N., "Quasi-Holographic Techniques in the Microwave Region", Proc. IEEE, Vol. 59, p. 1305, September 1971; and Brown, W. M. and L. J. Porcello, "An Introduction to Synthetic Aperture Radar", IEEE Spectrum, Vol. 6, p. 52, September 1969.
In range-Doppler imaging, fine range resolution is obtained by transmitting a signal that has a wide frequency band width. Doppler frequency resolution, and hence crossrange resolution, is inversely proportional to the coherent integration time interval.
In the usual analysis of range-Doppler imaging, the distance and relative motion between a point scatterer and the radar antenna is assumed to modify the received signal by a constant unknown time delay and Doppler frequency, respectively. However, more elaborate interactions between the object and transmitted signal occur if the coherent integration time is longer than the time required for object points to move through resolution cells, as is documented in Brown, W. M., "Synthetic Aperture Radar", IEEE Trans. on AES, Vol. 3, p. 217 (1967). Consequently, a simple time delay measurement and Doppler frequency analysis (Fourier transform) type of signal processing will result in degraded imagery if there is motion through resolution cells during an integration time interval.
As explained in Brown, W. M. and R. J. Fredericks, "Range-Doppler Imaging with Motion Through Resolution Cells", IEEE Trans. on AES, Vol. 5, p. 98 (1969), the problem of motion through resolution cells imposes the following resolution limitations: EQU .rho..sub.a.sup.2 &gt;.lambda.D.sub.r /4 EQU .rho..sub.a .rho..sub.r &gt;.lambda.D.sub.a /4
where: .rho..sub.a is crossrange resolution, .rho..sub.r is range resolution, D.sub.r is object width in range, and D.sub.a is object width in crossrange.
As a first approximation, the image aberrations which account for these resolution limitations are crossrange-dependent astigmatism and range-dependent crossrange focus error, also known in the art as "range walk" and "variable range rate", respectively.
To avoid these resolution limitations it is necessary to compensate for the changing range and Doppler frequency associated with each object point as it moves with time along its circular trajectory in the range-Doppler plane.
When the range-Doppler imaging is done with coherent optical data processing techniques, such as of the type disclosed in Cutrona, et al, U.S. Pat. No. 3,519,331, the prior art has approached the problem of resolution limitation with optical compensation techniques, e.g., as discussed in Brown, W. M. and R. J. Fredericks, "Range-Doppler Imaging with Motion Through Resolution Cells", IEEE Trans. on AES, Vol. 5, p. 98 (1969) and Fredericks, R. M., Space Variant Filtering In Coherent Optical Data Processors, Ph. D. Dissertation, University of Michigan, 1970. These optical techniques provide only a partial compensation for the rotational motion of object points through resolution cells, require a less desirable frame-by-frame approach to data processing, and are difficult to implement.
Another prior art optical compensation technique involves sectional processing in which lens adjustments are made in the optical processor to compensate for range-dependent crossrange focus error and for crossrange-dependent astigmatism error in one section of the scene. But a different adjustment is required to optimize the resolution of each section of the scene. The final image produced by photographically summing individually processed sections is only partially compensated and contains much image distortion.
Thus it is an object of the present invention to provide a technique for improving the resolution of a range-Doppler imaging system that provides compensation for motion through resolution cells in a convenient and effective manner, without the disadvantages of prior art techniques.